Chronic wounds affect millions of patients worldwide, and it is estimated that this number will increase steadily in the future due to population ageing. The research of new therapeutic approaches to wound healing includes the development of nanofibrous meshes and the use of platelet lysate (PL) to stimulate skin regeneration. This study considers a combination of a degradable electrospun nanofibrous blend of poly(L-lactide-co-ε-caprolactone) and poly(ε-caprolactone) (PLCL/PCL) membranes (NF) and fibrin loaded with various concentrations of PL aimed at the development of bioactive skin wound healing dressings. The cytocompatibility of the NF membranes, as well as the effect of PL, was evaluated in both monocultures and co-cultures of human keratinocytes and human endothelial cells. We determined that the keratinocytes were able to adhere on all the membranes, and their increased proliferation and differentiation was observed on the membranes that contained fibrin with at least 50% of PL (Fbg + PL) after 14 days. With respect to the co-culture experiments, the membranes with fibrin with 20% of PL were observed to enhance the metabolic activity of endothelial cells and their migration, and the proliferation and differentiation of keratinocytes. The results suggest that the newly developed NF combined with fibrin and PL, described in the study, provides a promising dressing for chronic wound healing purposes.